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Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment

Ze Chen, Shaode Yu

TL;DR

This work tackles blind image quality assessment (BIQA) in high-dimensional feature regimes where Kolmogorov-Arnold Networks (KAN) struggle. It introduces TaylorKAN, which replaces KAN's B-spline activations with a truncated Taylor expansion to enable local, efficient function approximation, and combines PCA-based dimensionality reduction with auto-configured network depth. Evaluations on five authentic distortion BIQA datasets (BID, CLIVE, KonIQ, SPAQ, FLIVE) show TaylorKAN achieving state-of-the-art or competitive performance among KAN variants, with strong inter-database generalization. Overall, TaylorKAN demonstrates that simple, local Taylor-based activations, coupled with dimensionality reduction and automatic architecture tuning, can deliver robust high-dimensional score regression for BIQA and related tasks.

Abstract

Kolmogorov-Arnold Network (KAN) has attracted growing interest for its strong function approximation capability. In our previous work, KAN and its variants were explored in score regression for blind image quality assessment (BIQA). However, these models encounter challenges when processing high-dimensional features, leading to limited performance gains and increased computational cost. To address these issues, we propose TaylorKAN that leverages the Taylor expansions as learnable activation functions to enhance local approximation capability. To improve the computational efficiency, network depth reduction and feature dimensionality compression are integrated into the TaylorKAN-based score regression pipeline. On five databases (BID, CLIVE, KonIQ, SPAQ, and FLIVE) with authentic distortions, extensive experiments demonstrate that TaylorKAN consistently outperforms the other KAN-related models, indicating that the local approximation via Taylor expansions is more effective than global approximation using orthogonal functions. Its generalization capacity is validated through inter-database experiments. The findings highlight the potential of TaylorKAN as an efficient and robust model for high-dimensional score regression.

Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment

TL;DR

This work tackles blind image quality assessment (BIQA) in high-dimensional feature regimes where Kolmogorov-Arnold Networks (KAN) struggle. It introduces TaylorKAN, which replaces KAN's B-spline activations with a truncated Taylor expansion to enable local, efficient function approximation, and combines PCA-based dimensionality reduction with auto-configured network depth. Evaluations on five authentic distortion BIQA datasets (BID, CLIVE, KonIQ, SPAQ, FLIVE) show TaylorKAN achieving state-of-the-art or competitive performance among KAN variants, with strong inter-database generalization. Overall, TaylorKAN demonstrates that simple, local Taylor-based activations, coupled with dimensionality reduction and automatic architecture tuning, can deliver robust high-dimensional score regression for BIQA and related tasks.

Abstract

Kolmogorov-Arnold Network (KAN) has attracted growing interest for its strong function approximation capability. In our previous work, KAN and its variants were explored in score regression for blind image quality assessment (BIQA). However, these models encounter challenges when processing high-dimensional features, leading to limited performance gains and increased computational cost. To address these issues, we propose TaylorKAN that leverages the Taylor expansions as learnable activation functions to enhance local approximation capability. To improve the computational efficiency, network depth reduction and feature dimensionality compression are integrated into the TaylorKAN-based score regression pipeline. On five databases (BID, CLIVE, KonIQ, SPAQ, and FLIVE) with authentic distortions, extensive experiments demonstrate that TaylorKAN consistently outperforms the other KAN-related models, indicating that the local approximation via Taylor expansions is more effective than global approximation using orthogonal functions. Its generalization capacity is validated through inter-database experiments. The findings highlight the potential of TaylorKAN as an efficient and robust model for high-dimensional score regression.

Paper Structure

This paper contains 35 sections, 15 equations, 5 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. TaylorKAN
  3. Kolmogorov-Arnold representation Theorem
  4. The first KAN model
  5. The proposed TaylorKAN model
  6. The difference between KAN and TaylorKAN
  7. Computational complexity
  8. Materials and Methods
  9. Databases
  10. High-dimensional feature collection
  11. TaylorKAN-based score regression
  12. Dimensionality reduction
  13. Auto-configuration of TaylorKAN
  14. Performance metrics
  15. Implementation details
  16. ...and 20 more sections

Figures (5)

  • Figure 1: Architectures of KAN and TaylorKAN.
  • Figure 2: The effect of changing variance ratio $V_{ratio}$ on the number of remaining PCs.
  • Figure 3: The effect of Taylor expansion orders on score regression.
  • Figure 4: Performance of TaylorKAN across different learning rates.
  • Figure 5: The distribution of MOS values of the five image databases.